Near optimal control for singularly perturbed systems with small time-delay

The near optimal control design for singularly perturbed systems with small time-delay is proposed. Based on the slow-fast decomposition theory of singular perturbations, the system is first decomposed into a fast subsystem and a slow time-delay subsystem. Then, the perturbation approach is proposed to solve the slow-time scale time-delay optimal control problem. The near optimal control law obtained consists of exact term and approximate one. The former can be found by solving a Riccati equation, and the latter can be approximately obtained by an iterative formula of adjoint vector equations. A numerical example is presented to illustrate the effectiveness of the proposed design approach.